How this calculator works
Radius of gyration measures how area is distributed about an axis: sqrt(I/A). Divide effective length by that radius to obtain slenderness. The built-in end factors are ideal elastic values. A custom factor accommodates a separately analysed frame. The same unbraced length and factor are used about both axes. Angle-section results refer to centroidal axes parallel to the legs; an unsymmetric column also needs principal-axis and torsional buckling checks.
Formula
rx = sqrt(Ix/A); ry = sqrt(Iy/A); lambda_x = K L/rx; lambda_y = K L/ry.
Worked example
A 100 mm by 200 mm rectangle has ry = 28.8675 mm. With L = 3 m and pinned ends, its weak centroidal-axis slenderness is 103.923. Fixed-fixed ends halve it to 51.9615.
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Frequently asked questions
Which axis governs?
For equal effective lengths, the axis with smaller radius of gyration gives larger slenderness.
What about a free-free column?
An unsupported member has rigid-body freedom rather than the laterally supported column assumed here. Use a structural model for its actual restraints.
Is the ideal K enough for a building column?
No. Frame sidesway, end stiffness and code requirements can change effective length.